The day after the special lecture. As always, I was in the school research lab, reading a grimoire. About an hour passed like that when, Creeak.
The door opened, and Giuseppe came in for the day.
He spoke.
"Junior... I told you, you don't need to come in this early."
"There's not much to do in my room anyway."
Heh heh.
Giuseppe let out a dry laugh.
"Well, thank you. I'm always grateful."
"...?"
"By the way, how was the special lecture yesterday? Sir Valerius is known for giving unusual tests every week, so I'm curious."
"Senior... you knew all along?"
Then why on earth didn't he tell me?
"I couldn't help it. If I had told you beforehand, Valerius would have surely come looking for me."
"Ah."
Now I get it. Being pursued by a Great Mage is a little scary. After that, I explained what happened yesterday.
From the two shadow tricks to the strange assignment I received at the end. After hearing the whole story, Giuseppe nodded.
"Just like him. So, what are you going to do for the next assignment? To discuss 'that which is impossible with magic'..."
"I know..."
I shared what I had been thinking about all last night. My original plan was quite grand. I had intended to apply 'Gödel’s Incompleteness Theorem' to magic...
But I gave up. This world didn't yet have the mathematical logic to support such a proof. If I said something too complicated, it would obviously be dismissed as incomprehensible nonsense.
"So, I prepared something a little simpler."
I took out a single sheet of parchment I had written overnight and handed it to Giuseppe.
"How about this?"
"Shorter than I thought."
Giuseppe took the parchment.
Tick, tock.
Inside the research lab where only the sound of a clock could be heard, Giuseppe read through my writing. A moment later, his mouth opened.
"This is..."
His hand trembled slightly.
"Magnificent. It's clear, and beautiful." ...
Is it that good?
Fortunately, the second week's special lecture didn't start with 'find the classroom'. We were gathered in a proper lecture hall, waiting for Valerius. The students around me were murmuring.
"We're not first-year undergrads, what kind of assignment is this?"
"... You sound pretty confident."
"Nope. I totally bombed it."
Watching them snicker amongst themselves reminded me of my past life. 'Their assignment was about what magic is... The more I think about it, the more garbage the topic is.
It's been a little over a year since I was reincarnated, how would I know what magic is? A moment later, Valerius appeared, and the special lecture began.
"Now then, submit the assignment I mentioned last time."
The students, one by one, placed thick bundles of parchment on Valerius's desk. 'Wow... look how thick those are.' Everyone must have worked really hard.
Mine is so thin... Is this okay? 'I should probably hand it in after class.'
If I turn it in now, I'll draw way too much attention. Valerius glanced through the students' assignments and spoke.
"This trash... no, I'll read these assignments later when I'm bored."
Didn't he just say trash...? I guess I wasn't the only one who heard it. One of the students, with a scowl on his face, shot his hand up.
"... Doing the assignment made me curious. Professor, what do you think magic is?"
Anyone could tell that was a protest. It had the feeling of, 'You call our work trash? Just how great are you?'
"A good question. 'What is magic'." ...
However, Valerius didn't interpret the student's political rhetoric at all. Valerius walked to the front of the chalkboard.
"Explaining with words is boring, so I'll give you an example."
He picked up a piece of chalk and began to draw an intricate magic circle on the board. Circles were layered one upon another, densely packed with rune symbols. Counting one circle for each level, seven circular magic circles were drawn concentrically.
"Seven circles. A 7th-circle spell..."
"I've never seen a structure like that."
"Did he create it himself?"
The students couldn't decipher the magic circle Valerius had drawn. ... To be honest, neither could I. 'It is quite abstruse.' It was a spell that most mages wouldn't even dare to touch.
Once the magic circle was complete, Valerius looked at us and spoke.
"What kind of spell do you think this is? Anyone can answer."
"... Hmm. Meteor-fall?"
"The sixth circle does contain a structure borrowed from that spell. Partially correct. Any other answers?"
Valerius went through the students one by one, listening to their answers.
"It must be a spell related to potion brewing."
"You saw the structure in the fourth circle."
"It seems to be something that makes an object move at a constant velocity."
"You deciphered the seventh. Not bad."
But the correct answer never came, and my turn arrived.
"Last one, disciple of Doloren. What do you think?"
"..."
"..."
Should I say it or not? Thanks to the students buying me time, I was able to decipher the spell. 'But how should I explain this...'
It was a bit awkward.
Pfft. Valerius laughed.
"Don't pretend you don't know. Fine. Then I'll show you directly."
Valerius poured his mana into the magic circle.
"Behold."
The entire magic circle shone with a brilliant light. The other students were probably expecting some incredible grand magic. But what appeared was...
Fwoosh.
A single small fireball. Valerius showed us the fireball on his palm.
"Huh...?"
"Did the magic circle fail to activate?"
"No way... this is Sir Valerius we're talking about."
Murmur, murmur.
Just then, Valerius's gaze turned to me.
"Disciple of Doloren. Tell me. Why did this spell manifest in this way?"
All eyes turned to me.
'Damn it...'
I should have said something earlier. I would have gotten less attention then. It can't be helped.
Since it's come to this, I'll just say it. I took the chalk from Valerius and stood before the chalkboard.
"So... this is a kind of recursive question-type spell."
To my eyes, that magic circle looks like this. 'Regarding whether it is permissible to voice the question about requiring approval for asking for permission to use a fireball...'
It's horrible.
To think it was a recursive question-type spell... At my explanation, one of the students spoke up.
"... If that were the case, there's no way we wouldn't have known."
"That would be true if it were just a simple list of negations. But this spell hides its structure by turning it into a kind of 'module'."
I checked each part of the magic circle.
"Do you see? It mixes abbreviations used by different schools, but after the calculations for each part are done, there are almost no resulting values left."
Each school in the Magic Tower uses different abbreviations and operators for 'confidentiality' reasons. This spell took advantage of that fact to create a large number of operators that cancel each other out in the final process. I erased those 'fake structures' one by one.
First, second, and seventh circles, cleared.
"Whoa..."
"It's real. They're being erased."
Third, fifth, and sixth circles, also cleared.
"If this keeps up, the only thing left will be..."
"Just the fourth circle."
After erasing everything that could be erased from the fourth circle as well... Within the seven large circles, only the most basic framework of a fireball spell remained, looking bare. I channeled mana only into the remaining parts and activated the magic circle.
Fwoosh.
A fireball formed once again. I turned my gaze to Valerius.
"Is this correct?"
Valerius nodded his head.
"It is."
Hooo.
A sigh escaped me. I really hate presentations. I quickly returned to my seat.
Valerius pointed to the chalkboard and said, "As you've all seen, when the logic is twisted, the result becomes ridiculous. Magic, in the end, is nothing more than a logic puzzle." Gasps of admiration erupted from here and there.
It seemed everyone had some kind of realization.
"It seems we're finally at the starting line. In that case, here is a question."
At a gesture from Valerius, the chalkboard with the magic circle drawn on it flipped over.
Fwip.
"If the basis of magic is logic, what happens when you pursue its limits?"
On the back of the chalkboard, a strange magic circle was drawn.
"Now. This is the first lesson. Experience it for yourselves."
The moment Valerius poured his mana into the magic circle. My vision turned white.
Dizzy.
I suppressed my vertigo and stood up.
"What is this..."
In front of my eyes was a white marble track. This is absurd.
"Is something like this even possible with magic?"
Looking around, I saw the other students who had been in the special lecture with me.
"Is it an enemy attack?!"
"Ugh, damn. My head feels like it's going to split open."
It seemed no one could grasp the situation. Just then, Valerius's voice echoed from the sky. -"Welcome. This is a magical space where 'logic' governs the laws."
He continued his explanation. -"Do you see the tortoise ahead?" As he said, a small tortoise was visible in front of us students.
Crawl, crawl.
The creature was crawling along the track at a very slow pace. -"You can probably walk ten times faster than that tortoise. However, you will never be able to overtake it."
Ah.
Could it be that? Valerius continued. -"By the time you reach the point where the tortoise was, the tortoise will have already moved forward in that time."
'Achilles and the Tortoise'.
It was a paradox that had troubled Earth's intellectuals for a long time. -"To the one who gets out first, I shall grant a wish." As soon as Valerius finished speaking, cheers erupted from the students.
"A... a wish? From Sir Valerius?"
"Insane...!"
The promise of a Great Mage carries great weight. He would probably grant just about anything possible with his power.
"Begin!"
As soon as Valerius's shout fell, the students' eyes glinted like those of wild beasts. The first one to move was Gwendolyn.
"Wind, grant strength to my legs!"
She constructed her spell using a mix of hand signs and incantations. 'A spell to reduce air resistance and increase her stride?' Gwendolyn focused mana in her legs and shot forward faster than anyone else.
"What? Already?"
"A freshman skipping incantations... no way."
While the other students were exclaiming in admiration, Gwendolyn sprinted on. The distance to the tortoise wasn't that far.
"I've caught up!"
Therefore, she was easily able to reach the tortoise.
However... Crawl.
In the very next moment, the tortoise was slightly ahead of her.
"Huh...?"
Gwendolyn took another step forward. At the same time, the tortoise also moved a little further ahead.
Crawl.
"Huh???"
If she took a full step closer, it moved away. Even if she took a half step closer, it moved away... A quarter of a step was the same.
And so, for countless moments, the tortoise defended its position in front of her. The tortoise's sturdy back seemed to be saying. 'Think you can catch me?'
Meanwhile.
Valerius was looking down at the 'miniature racetrack model' on his desk. Inside it, small, doll-like students were desperately chasing a crystal turtle. He had told them to overtake the tortoise, but he didn't think they would succeed.
Magic is logic, and this miniature model is a prison of logic. Therefore, they would not be able to escape this prison with their own hands.
"If I just leave them for about 30 minutes and then let them out, they should learn something, right?"
He was just about to take a leisurely sip of his tea. But just then. Something unusual happened in the miniature racetrack model.
"...?"
Inside the miniature racetrack model, while the other students were still chasing after the tortoise... One person stood out. The small, black-haired doll, Isaac Upperhills, was the only one who had passed the crystal turtle.
Crawl, crawl.
No matter how much the model turtle walked, it couldn't catch up to Isaac's steps.
"Impossible..."
He almost dropped the teacup he was holding. The magic circle was perfect. There were no magical tricks, no physical deception.
The logic was supposed to be absolute. Because magic is logic.
"Then how..."
Did Isaac overcome the tortoise?